For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
I Have a Dream
When we meet up with our animal heroes, they're enduring tyrannical and miserable working conditions on Manor Farm. Luckily, one pig has a dream—and he manages to pass on his vision of an animal-run farm right before dropping dead.
And the successful revolution brings us right up to…
Act II
A Dream Deferred
Disaster befalls the animals as the leadership begins to take advantage of, well, its leadership role. Oh, and then the windmill collapses, and everyone's starving. And then the human blow up the resurrected windmill and… everyone's starving.
Act III
Working for the Weekend
The animals work hard, but it's not hard enough. Gradually, the pigs become more and more exploitative until—presto, change-o!—they start to look indistinguishable from the humans. Moral of the story: don't let pigs become your leaders. (Make them into bacon, instead.)